There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the... Plane Geometry - Page 72by John Charles Stone, James Franklin Millis - 1916 - 278 pagesFull view - About this book
| George Albert Wentworth - Geometry - 1877 - 416 pages
...THEOREM. 106. Two triangles are equal in all respects when two sides and the included angle of the **one are equal respectively to two sides and the included angle of the other. D** Ai In the triangles ABC and A' B' C', let AB = A' B', AC = A' C', ZA = Z A'. We are to prove AABC =... | |
| George Anthony Hill - Geometry - 1880 - 348 pages
...and the inFif' '°°' cluded angle completely determine a Theorem. — Two parallelograms are equal **if two sides and the included angle of one are equal respectively to two sides and the included angle** of the other. Exercises. — 1. Construct a parallelogram, the two sides being 44™ and 66°°, and... | |
| Webster Wells - Geometry - 1886 - 392 pages
...672. Two triangles on the same sphere or on two equal spheres are either equal or symmetrical when **two sides and the included angle of one are equal respectively to two sides and the included angle** of the other. I. In the triangles ABC and DEF, let the sides AB and AC and the included angle A be... | |
| George Anthony Hill - Geometry - 1888 - 202 pages
...? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, **if two sides and the included angle of one are equal,...respectively, to two sides and the included angle** of the other. HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. -^ BDE A ABC = A DEF. FI°- 67PROOF.... | |
| George Anthony Hill - Geometry - 1888 - 200 pages
...If two parts are given ? If the three angles are given ? 14. Theorem. — Two triangles are equal, **if two sides and the included angle of one are equal,...respectively, to two sides and the included angle** of the other, HYPOTHESIS. A ABC and DEF, AB=DE, AC CONCLUSION. A ABC = A DEF. PROOF. We may divide... | |
| George Anthony Hill - Geometry - 1889 - 200 pages
...given? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, **if two sides \ and the included angle of one are equal, respectively,** vto two sides and the included angle of the other, HYPOTHESIS. j} A ABC and DEF, AB=DE, AC=DF, CONCLUSION.... | |
| Education - 1893 - 568 pages
...triangle by measuring two sides and included angle of a given triangle. Theorem: Two triangles are equal **if two sides and the included angle of one are equal,...respectively, to two sides and the included angle** of the other. 13. Theorem: i. In an isosceles triangle, the angles opposite the equal sides are equal.... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...which is not in the right bisector of a straight line is unequally distant from the ends of the line. **and the included angle of one are equal respectively to two sides and the included angle** of the other. 146. Theorem. Two triangles are equal if two angles and a side of one are equal respectively... | |
| Webster Wells - Geometry - 1894 - 400 pages
...prove AB > BC — A C. We have AB + AC > BC. PROPOSITION XV. THEOREM. 63. Two triangles are equal when **two sides and the included angle of one are equal respectively to** tivo sides and the included angle of the other. a ABDE In the triangles ABC and DEF, let AB = DE, AC... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...greater face angle. PROPOSITION XXVI. THEOREM &73. Two triangles on the same sphere are equal : I. **If two sides and the included angle of one are equal respectively to two sides and the included angle** of the other. II. If a side and the two adjacent angles of one are equal respectively to a side and... | |
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